Example 7
Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 4’ given that ‘there is at least one tail’.
A coin is tossed. if the coin shows head, it is tossed again. If it shows tail, then a die is thrown.
Hence different value of probabilities are
We need to find the probability that the die shows a number greater than 4, given that there is at least one tail.
Now, F : Number greater than 4 on the die
E : at least one tail
We need to find P(E|F)
Also, E ∩ F = {(T, 5), (T, 6)}
So, P(E ∩ F) = P(T, 5) + P(T, 6)
So, P(E ∩ F) = P(T, 5) + P(T, 6)
= 1﷮12﷯ + 1﷮12﷯
= 2﷮12﷯ = 1﷮6﷯
Now,
P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯
= 1﷮6﷯﷮ 3﷮4﷯﷯
= 1﷮6﷯ × 4﷮3﷯
= 𝟐﷮𝟗﷯
Therefore, required probability is 2﷮9﷯